Ergodic properties of integral points on ellipsoids of genus

The ergodic and the intermixing theorems of Yu. V. Linnik (Mat. Sb.,43, No. 2, 257–276) are generalized to arbitrary positive quadratic forms of genus of , where Ω > 1 is an odd number, of invariants [Ω,1], defined by the character for all prime numbers ρ¦Ω. One obtains estimates for the remainder term. The method of proof is simplified.